One thing that confused me when I was a student was the two ways of spelling the color intermediate between white and black; namely, gray, or grey. Both spellings are "correct," but grey is the common usage in the United Kingdom, and gray is the common United States spelling. You can confirm this on Wikipedia, where your search for "gray" redirects you to the page for "grey." The English language Wikipedia is a great resource, but it has an Anglophile bias. I discovered this when searching for "jewelry" many years ago and ended up on a page for "jewellery." It's interesting to note the spelling of "Fifty Shades of Grey" in the novel and film. Google reports twice the number of hits for gray than grey.

Grey goo must have a prime directive to not use others of itself as feedstock; and, perhaps, another directive that allows teams of devices to cooperate in processes to their mutual benefit. computer scientists and robotics experts have harnessed the power of device cooperation to create swarms of useful objects. The venerable IEEE, of which I am a member, has published many articles about swarm robots in IEEE Spectrum. Here's a sampler of articles, all written by Evan Ackerman.

The simple expanding/contractingrobotic particle on the left can act in concert with other such particles to move within a plane in response to a stimulus. (Left image from a Columbia University YouTube Video by Richa Batra, Shuguang Li, Jane Nisselson, Kyle Parsons/Columbia Engineering. Right image by Shuguang Li/Columbia Engineering,)

Conventional robotic swarms operate with a programmed coordinated motion in which each member is an independently functioning machine that's given explicit movement commands. As a consequence, the failure of a very small number of the swarm members renders the swarm inoperable.[3-4] In contrast, biological organisms are more robust since their high-level behavior is achieved through coordinated action of their components operating stochasticly.[3] The research team showed that this same stochastic, statistical mechanical operating principle can be programmed into particle robots that respond to stimuli without specific programming.[3]

The individual robotic particles perform only uniform volumetricoscillations of expansion and contraction that are phase-modulated by a stimulus signal such as a light source.[3-4] In response to a light source, each robot measures the light intensity, broadcasts its value to the group, and then receives the light intensity sensed by its neighbors to determine the phase delay of its motion. The delays result in a motion towards the light source.[4]

The robot particles closer to the light are designed to start their volume pulsing cycle earlier, and this creates a motion wave throughout the cluster that drives the cluster towards the light. Although the individual robot particles cannot move independently, but only shrink or swell, the light stimulus creates a global motion.[4] This was verified experimentally with a group of up to two dozen robots, and more complex motions were investigated in computer simulations of up to 100,000 robots.[3] Transport of objects was also realized.[3]

A computer simulation of barrier penetration by an assemblage of many robotic particles. The mass of particles streams through a small opening in a barrier. (Still images from a Columbia University YouTube Video by Richa Batra, Shuguang Li, Jane Nisselson, Kyle Parsons/Columbia Engineering.)

"You can think of our new robot as the proverbial 'Gray Goo'... "Our robot has no single point of failure and no centralized control. It's still fairly primitive, but now we know that this fundamental robot paradigm is actually possible. We think it may even explain how groups of cells can move together, even though individual cells cannot... We've been trying to fundamentally rethink our approach to robotics, to discover if there is a way to make robots differently... Not just make a robot look like a biological creature but actually construct it like a biological system, to create something that is vast in complexity and abilities yet composed of fundamentally simple parts."[4]

Such a system is robust against the failure of individual components. This was demonstrated also in simulations of obstacle avoidance and object transport with hundreds and thousands of particles.[4] The particle robot collective maintained roughly half its speed when as many as 20% of its members were dormant.[4] Says Lipson, "We think it will be possible one day to make these kinds of robots from millions of tiny particles, like microbeads that respond to sound or light or chemical gradient... Such robots could be used to do things like clean up areas or explore unknown terrains/structures."[4] This research was supported by the Defense Advanced Research Projects Agency and the National Science Foundation.